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In the chapter 957 titled “Ultimate” we got this panel of Gol D. Roger and Monkey D. Garp vs. Rocks D. Xebec:

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So I realized that Roger’s sword looks almost identical to the sword Gryphon held by Shanks.

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Gryphon is a durable and powerful sword, being capable of clashing equally with Whitebeard’s naginata, the Murakumogiri, which made the sky split apart.

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When imbued with Haki, it was strong enough to block Sakazuki’s magma fist without taking any damage.

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Unless Shanks has a near identical sword then I figure they’re the same. So Gryphon originally belonged to Gol D. Roger just like the straw hat.

*Theory by XraynPR